Robertson emigrated to Australia from Dublin with his fellow apprentice bookseller, Samuel Mullen. He set up business as a bookseller and publisher and in 1855 Mullen joined him as an assistant. In 1857 Robertson set up a branch in London. He and Mullen became permanently estranged as a result of Robertson's decision to give the job of managing the London office to his brother, William, rather than Mullen.
From 1860 Robertson opened bookshops in Melbourne, Adelaide, Sydney and Brisbane. His firm published works by many leading Australian writers. From 1861-1889 he published George Robertson's Monthly Book Circular, as well as the Melbourne Review (1879-1885) and the Tatler (1897-1898).
Robertson retired in 1890. In 1922 his firm merged with Melville & Mullen to become Robertson & Mullens.